Skip to main content
guest
Join
|
Help
|
Sign In
xenharmonic (microtonal wiki)
Home
guest
|
Join
|
Help
|
Sign In
Actions
Wiki Home
Projects
Recent Changes
Pages and Files
Members
Navigation
Introduction
Help
(
Conventions
)
Languages
Deutsch
English
Español
日本語
Connect
XA Facebook Group
XA IRC Chat
Practice
Instruments
Software
Pedagogy
Listen
Scores
Discussion
People
Projects
Theory
Orientation
General Theory
Mathematical Theory
Useful Tools
Lists and Galleries
Backing up this wiki
Temperament lattice bases
Edit
0
17
…
5
Tags
lattice
overview
table
temperaments
todo:link
Notify
RSS
Backlinks
Source
Print
Export (PDF)
Below are tabulated bases (temperamental Minkowski bases) of minimal temperamental complexity for the pitch classes of various regular temperaments.
Rank Three
Seven limit
Comma
Name
Gen 1
Length
Gen 2
Length
Angle
686/675
Keema
15/14
0.6977
3/2
1.4208
103.732
64/63
Archytas
3/2
1.0508
5/4
2.3219
90.000
875/864
Keema
6/5
0.8879
3/2
1.3391
77.834
81/80
Didymus
3/2
0.5451
8/7
2.8074
90.000
3125/3087
Gariboh
25/21
0.5928
21/20
1.2018
80.810
2430/2401
Nuwell
7/6
0.6247
9/7
1.1894
94.044
50421/50000
Trimyna
7/5
0.3158
5/4
1.7938
94.101
245/243
Sensamagic
3/2
0.9644
9/7
1.0807
96.914
126/125
Starling
6/5
1.068
5/4
1.206
100.364
4000/3969
Octagar
63/50
0.8966
21/20
1.0605
97.743
1728/1715
Orwellisma
7/6
0.7526
3/2
1.3931
97.508
1029/1024
Gamelisma
8/7
0.5192
5/4
2.3219
90.000
225/224
Marvel
16/15
1.256
3/2
1.369
106.958
3136/3125
Hemimean
28/25
0.5055
3/2
1.5849
90.000
5120/5103
Hemifamity
3/2
0.5670
10/9
1.8063
82.112
6144/6125
Porwell
35/32
0.9584
35/24
1.1877
92.681
65625/65536
Horwell
5/4
0.6213
16/15
1.3863
64.638
703125/702464
Meter
75/56
0.7305
375/224
0.7675
97.289
420175 / 419904
Wizma
245/216
0.5541
324/245
0.9731
79.663
2401/2400
Breedsma
49/40
0.7858
8/7
1.1241
107.367
4375/4374
Ragisma
10/9
0.7890
6/5
0.9208
105.299
Eleven limit
Commas
Name
Gen 1
Length
Gen 2
Length
Angle
225/224&385/384
Marvel
16/15
1.0364
5/4
1.0759
104.028
225/224&441/400
Prodigy
16/15
0.9111
3/2
0.9477
65.933
99/98&176/175
Minerva
16/15
0.8997
5/4
1.0457
98.604
126/125&176/175
Thrush
5/4
0.8576
6/5
0.9314
74.624
56/55&100/99
Thrasher
6/5
0.9089
5/4
1.2007
98.845
Javascript Required
You need to enable Javascript in your browser to edit pages.
help on how to format text
Help
·
About
·
Pricing
·
Privacy
·
Terms
·
Support
Contributions to https://xenharmonic.wikispaces.com/ are licensed under a
Creative Commons Attribution Share-Alike Non-Commercial 3.0 License
.
Portions not contributed by visitors are Copyright 2018 Tangient LLC
TES: The largest network of teachers in the world
Turn off "Getting Started"
Home
...
Loading...
Rank Three
Seven limit
Eleven limit